Problem: Solve for $x$ and $y$ using elimination. ${3x-6y = -18}$ ${x-5y = -18}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${3x-6y = -18}$ $-3x+15y = 54$ Add the top and bottom equations together. $9y = 36$ $\dfrac{9y}{{9}} = \dfrac{36}{{9}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {3x-6y = -18}\thinspace$ to find $x$ ${3x - 6}{(4)}{= -18}$ $3x-24 = -18$ $3x-24{+24} = -18{+24}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 4}$ into $\thinspace {x-5y = -18}\thinspace$ and get the same answer for $x$ : ${x - 5}{(4)}{= -18}$ ${x = 2}$